Pure components, calculating state-dependent activity

At present there are two fundamentally different approaches available for calculating phase equilibria, one utilising activity coefficients and the other an equation of state. In the case of vapour-liquid equilibrium (VLE), the first method is an extension of Raoult s Law. For binary systems it requires typically three Antoine parameters for each component and two parameters for the activity coefficients to describe the pure-component vapour pressure and the phase equilibrium. Further parameters are needed to represent the temperature dependence of the activity coefficients, therebly allowing the heat of mixing to be calculated. 

To apply this method, the Uquid molar volumes of the mixture and of the pure components need to be known. At a given pressure and temperature these values can be calculated from the equation of state. However, since sji according to Eq. (63) is volume-dependent, this involves an iterative procedure similar to that described by Danner and High [4] for the method of Chen et al. [50]. Eigure 2.12 shows the experimental solvent activity of the system poly(propylene oxide)-benzene at 347.85 K compared to the correlation by UNIQUAC and predictions by the GC-Flory model. The result of the correlation is almost perfect. The predicted solvent activities by the GC-Elory model are also very cJose to the experimental values. In Figure 2.13 a comparison is shown of experimental solvent activity... 

The quality of all model calculations with respect to solvent activities depends essentially on the careful determination and selection of the parameters of the pure solvents, and also of the pure polymers. Pure solvent parameter must allow for the quantitative calculation of pure solvent vapor pressures and molar volumes, especially when equation-of-state approaches are used. Pure polymer parameters strongly influence the calculation of gas solubilities, Henry s constants, and limiting solvent activities at infinite dilution of the solvent in the liquid/molten polymer. Additionally, the polymer parameters mainly determine the occurrence of a demixing region in such model calculations. Generally, the quantitative representation of liquid-liquid equilibria is a much more stringent test for any model, what was not discussed here. To calculate such equilibria it is often necessary to use some mixture properties to obtain pure-component polymer parameters. This is necessary because, at present, no single theory is able to describe correctly the properties of a poly-... 

Wilson s equation of state is found from Equations (14) and (15). It can be seen that for obtaining the activity coefficient of a component 1 in a pure solvent 2, we need four interaction parameters (A12, A21, An a A22, which are temperature dependent. It is evident that for calculating the value of the binary interaction parameters, additional experimental data, such as molar volume is needed. Other models which belong to the first category have the same limitations as Wilson s method. The Wilson model was used in the prediction of various hydrocarbons in water in pure form and mixed with other solvents by Matsuda et al. [11], In order to estimate the pure properties of the species, the Tassios method [12] with DECHEMA VLE handbook [13] were used. Matsuda et al. also took some assumptions in the estimation of binary interactions (because of the lack of data) that resulted in some deviations from the experimental data. 

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